I might be mistaken but isn't the House deciding only for ties? There is no majority but there is a clear first place. I don't think it goes to House in that case.
The Twelfth Amendment states that is no one has a majority of the electoral votes it goes to the House of Representatives. Though I think they have it that the Representatives from each State get one vote between them, so would assuredly vote amongst themselves. There is not going to be a Progressive Party President in this place unless the Constitution was altered a lot or if there is political horse trading. They have a lot of votes here, but that is still only something like a third of voters. Hell, there having Florida, New York, California, and Texas doesn’t help too much since those are only four votes, and they might not have majorities of the Representatives in those states anyways. Thinking over it, this map could probably be used as an example on how many different systems of government work, as well as why there are not as many parties in the Us as there are in parliamentary states.